Inverse
Lagrange’s Interpolation Formula
Theory
:
.
Example :
1.
Use Lagrange’s inverse interpolation formula to obtain the value of t, when
A=85 from the following table-------------
T
|
2
|
5
|
8
|
14
|
A
|
94.8
|
87.9
|
81.3
|
68.7
|
Ans : 6.30383001716033
2.
Lagrange’s formula inversely to obtain the value of ɸ, when F(ɸ)=0.3887, from
the following table----------
ɸ
|
210
|
230
|
250
|
F(ɸ)
|
0.3706
|
0.4068
|
0.4433
|
Ans : 220.020463153135
3. Find the value of x
corresponding to y=1000, by using inverse interpolation, from the given data.
X
|
3
|
5
|
7
|
9
|
Y
|
6
|
24
|
58
|
108
|
Ans
: 6139.30475615886
4. Find the
age-corresponding to the annuity value 13.6 given
Age(x)
|
30
|
35
|
40
|
45
|
5 0
|
Annuity
value(y)
|
15.9
|
14.9
|
14.1
|
13.3
|
12.5
|
Ans
: 43.1418504901961
5.
The following table gives the value of the probability integral equal to 0.5
X
|
0.46
|
0.47
|
0.48
|
0.49
|
F(x)
|
0.4846555
|
0.4937452
|
0.5027498
|
0.51166833
|
Ans
: 0.476936
6. Apply Lagrange’s formula inversely
to obtain the root of the equation f(x)=0,given
f(30)=-30, f(34)=-13, f(38)=3,
f(42)=18.
Ans : 37.230373
7. Apply Lagrange’s inverse
interpolation, from the data given below, find the value of x , when y=13.5.
X
|
93.0
|
96.2
|
100.0
|
104.2
|
108.7
|
Y
|
11.38
|
12.80
|
14.70
|
17.07
|
19.91
|
Ans : 97.555746
Algorithm for Inverse Lagrange interpolation formula--------
Flow chart for Inverse Lagrange Interpolation formula :
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